Liquid–liquid micro-dispersion in a double-pore T-shaped microfluidic device

For further understanding the dispersion process in the T-shaped microfluidic device, a double-pore T-shaped microchannel was designed and tested with octane/water system to form monodispersed plugs and droplets in this work. The liquid–liquid two-phase flow patterns were investigated and it was found that only short plugs, relative length L/w < 1.4, were produced. Additionally, the droplets flow was realized at phase ratios (F _C /F _D) just higher than 0.5, which is much smaller than that in the single-pore T-shaped microchannels. A repulsed effect between the initial droplets was observed in the droplet formation process and the periodic fluctuation flow of the dispersed phase was discussed by analyzing the resistances. Besides, the effect of the two-phase flow rates on the plug length and the droplet diameter was investigated. Considering the mutual effect of the initial droplets and the equilibrium between the shearing force with the interfacial tension, phase ratio and Ca number were introduced into the semi-empirical models to present the plug and droplet sizes at different operating conditions.     

Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping

In this work, we have systematically analyzed the scaling law of droplet formation by cross-flow shear method in T-junction microfluidic devices. The droplet formation mechanisms can be distinguished by the capillary number for the continuous phase (Ca_c), which are the squeezing regime (Ca_c < 0.002), dripping regime (0.01 < Ca_c < 0.3), and the transient regime (0.002 < Ca_c< 0.01). Three corresponding correlations have been suggested in the different range of Ca_c. In the dripping regime, we developed a modified capillary number for the continuous phase (Ca_c′) by considering the influence of growing droplet size on the continuous phase flow rate. And the modified model could predict droplet diameter more accurately. In the squeezing regime, the final plug length was contributed by the growth and ‘squeeze’ stages based on the observation of dynamic break-up process. In the transient regime, we firstly suggested a mathematical model by considering the influences of the above two mechanisms. The correlations should be very useful for the application of controlling droplet size in T-junction microfluidic devices.     

Droplet coalescence by geometrically mediated flow in microfluidic channels

Microfluidic flow is geometrically mediated at a trifurcating junction allowing periodically formed, equally spaced out emulsion droplets to redistribute and fuse consistently. This is achieved by controlling the ratio between the droplet transport time across the trifurcating junction and the drainage time of the fluid volume separating the droplets t _r/t _d. Three different microfluidic trifurcation geometries have been designed and compared for their droplet fusion efficiencies. Fusion of up to six droplets has been observed in these devices. The fusion of two droplets occurs when t _r/t _d is equal to 1.25 and the number of fused droplets increases with t _r/t _d. When the junction length (d) is 216 μm fusion of 2–6 six droplets are possible however when the junction length is increased to 360 μm fusion of only two droplets is observed.     

Generating gas/liquid/liquid three-phase microdispersed systems in double T-junctions microfluidic device

This article describes the generation of microdispersed bubbles and droplets in a double T-junctions microfluidic device to form immiscible gas/liquid/liquid three-phase flowing systems. Segmented gas plugs are controllably prepared in water at the first T-junction to form gas/liquid two-phase fluid with the perpendicular flow cutting method. Then using this two-phase fluid as the cross-shearing fluid for the oil phase at the second T-junction, the gas/liquid/liquid three-phase flowing systems are prepared. Interestingly, it is found that the break-up of the oil droplets is mainly dominated by the cutting effect of the gas/liquid interface or the pressure drop across the emerging droplet, but independent with the viscous shearing effect of the continuous phase, even at the capillary number (Ca = u _wμ_w/γ_ow) higher than 0.01. The size laws and the distributions of the bubbles and droplets are investigated carefully, and a mathematical model has been developed to relating the operating conditions with the dispersed sizes.     

Micro-droplet formation in non-Newtonian fluid in a microchannel

Micro-droplet formation from an aperture with a diameter of micrometers is numerically investigated under the cross-flow conditions of an experimental microchannel emulsification process. The process involves dispersing an oil phase into continuous phase fluid through a microchannel wall made of apertured substrate. Cross-flow in the microchannel is of non-Newtonian nature, which is included in the simulations. Micro-droplets of diameter 0.76–30 μm are obtained from the simulations for the apertures of diameter 0.1–10.0 μm. The simulation results show that rheology of the bulk liquid flow greatly affects the formation and size of droplets and that dispersed micro-droplets are formed by two different breakup mechanisms: in dripping regime and in jetting regime characterized by capillary number Ca. Relations between droplet size, aperture opening size, interfacial tension, bulk flow rheology, and disperse phase flow rate are discussed based on the simulation and the experimental results. Data and models from literature on membrane emulsification and T-junction droplet formation processes are discussed and compared with the present results. Detailed force balance models are discussed. Scaling factor for predicting droplet size is suggested.     

Monodisperse droplets by impinging flow-focusing

We proposed a new flow-focusing technique for generation of monodisperse femtoliter droplets, based on the capillary micro-cross. A funnel-shaped interface of two phase system is observed in a capillary cross for mass production of uniform drops, where a tapered exit orifice is extruded into the dispersed feeding capillary. The droplets, down to 2 μm in size at frequency of 20 kHz, are controllable in size when choosing orifice and capillary sizes, as well as flow rates of inner and outer fluids. For a specific diameter of exit orifice, there is a maximal flow rate of outer fluid, beyond which the interface will be penetrated. Until then, the interface is in steady state and all droplets are highly uniform (<3%), implicating an absolute instability in the whole process.     

Gas�Cliquid flow stability and bubble formation in non-Newtonian fluids in microfluidic flow-focusing devices

This communication describes the gas–liquid two-phase flow patterns and the formation of bubbles in non-Newtonian fluids in microfluidic flow-focusing devices. Experiments were conducted in two different polymethyl methacrylate (PMMA) square microchannels of, respectively, 600 × 600 and 400 × 400 μm. N₂ bubbles were generated in non-Newtonian polyacrylamide (PAAm) solutions of different concentrations. Slug bubble, missile bubble, annular and intermittent flow patterns were observed at the cross-junction by varying gas and liquid flow rates. Gas and liquid flow rates, concentration of PAAm solutions, and channel size were varied to investigate their effect on the mechanism of bubble formation. The bubble size was proportional to the ratio of gas/liquid flow rate for slug bubbles and could be scaled with the ratio of gas/liquid flow rate as a power–law relationship for missile bubbles under wide experimental conditions.     

Droplet formation by squeezing in a microfluidic cross-junction

In microfluidics, flow focusing is widely used to produce water-in-oil droplets in microchannels at high frequency. We here report an experimental study of droplet formation in a microfluidic cross-junction with a minimum number of geometrical parameters. We mostly focus on the squeezing regime, which is composed of two distinct steps: filling and pinching. The duration of each step (and corresponding volumes of each liquid phase) is analyzed. They vary according to both water and oil flow rates. These variations provide several insights about the fluid flows in both phases. We propose several scaling laws to relate the droplet volume and frequency to the flow rate of both phases. We also discuss the influence of surfactant and channel compliance on droplet formation.     

The spreading of a viscous microdrop on a solid surface

The spreading of a liquid microdrop across a solid surface is examined using the interface formation model. This model allows for variable surface tension at constant temperature and a flow induced Maragoni effect, by incorporating irreversible thermodynamics into the continuum model. The model is solved for small Capillary number and small Reynolds number. This problem has been considered before for much larger drops in Shikhmurzaev (Phys Fluids 9:266, 1997a), which examined the spreading of a drop for ε = τ U _CL/R ≪ 1, where U _CL is the speed of the moving contact line across the solid surface, τ is the surface tension relaxation time of the viscous liquid, and R is a typical length scale for the size of the drop. This paper extends that work by examining ε = O(1), which will be shown to be the appropriate scaling for very small liquid drops, on the scale of micrometres or less.     

Reliable addition of reagents into microfluidic droplets

This article reports a design that reliably adds reagents into droplets by exploiting the physics of fluid flow at a T-junction in the microchannel. An expanded section right after the T-junction enhances merging of a stream with a droplet, eliminates the drawbacks such as extra droplet formation and long mixing time. The expanded section reduces the pressure buildup at the T-junction and minimizes the tendency to form extra droplets; plays the role in creating low Laplace pressure jump across the interface of the droplet forming from the T-junction which reduces the probability of forming extra droplet in the merging process; provides space for droplet coalescence if there is an extra droplet due to droplet break-up before merging. In this design, after merging, the reactants are in axial arrangement inside the droplets which lead to faster mixing. Reliable addition of reagent to the droplets happens for the combination of flow rates in a broad range from 25 to 250 μl/h, for both DI water (Q _DI) and fluorescent (Q _fluo) streams.     

Analysis of capillary filling in nanochannels with electroviscous effects

Capillary filling is the key phenomenon in planar chromatography techniques such as paper chromatography and thin layer chromatography. Recent advances in micro/nanotechnologies allow the fabrication of nanoscale structures that can replace the traditional stationary phases such as paper, silica gel, alumina, or cellulose. Thus, understanding capillary filling in a nanochannel helps to advance the development of planar chromatography based on fabricated nanochannels. This paper reports an analysis of the capillary filling process in a nanochannel with consideration of electroviscous effect. In larger scale channels, where the thickness of electrical double layer (EDL) is much smaller than the characteristic length, the formation of the EDL plays an insignificant role in fluid flow. However, in nanochannels, where the EDL thickness is comparable to the characteristic length, its formation contributes to the increase in apparent viscosity of the flow. The results show that the filling process follows the Washburn’s equation, where the filled column is proportional to the square root of time, but with a higher apparent viscosity. It is shown that the electroviscous effect is most significant if the ratio between the channel height (h) and the Debye length (κ ⁻¹) reaches an optimum value (i.e. κh ≈ 4). The apparent viscosity is higher with higher zeta potential and lower ion mobility.     

Hybrid molecular dynamics-continuum simulation for nano/mesoscale channel flows

The present study deals with multiscale simulation of the fluid flows in nano/mesoscale channels. A hybrid molecular dynamics (MD)-continuum simulation with the principle of crude constrained Lagrangian dynamics for data exchange between continuum and MD regions is performed to resolve the Couette and Poiseuille flows. Unlike the smaller channel heights, H < 50σ (σ is the molecular length scale, σ ≈ 0.34 nm for liquid Ar), considered in the previous works, this study deals with nano/mesoscale channels with height falling into the range of 44σ ≤ H ≤ 400σ, i.e., O(10)–O(10²) nm. The major concerns are: (1) to alleviate statistic fluctuations so as to improve convergence characteristics of the hybrid simulation—a novel treatment for evaluation of force exerted on individual particle is proposed and its effectiveness is demonstrated; (2) to explore the appropriate sizes of the pure MD region and the overlap region for hybrid MD-continuum simulations—the results disclosed that, the pure MD region of at least 12σ and the overlap region of the height 10σ have to be used in this class of hybrid MD-continuum simulations; and (3) to investigate the influences of channel height on the predictions of the flow field and the slip length—a slip length correlation is formulated and the effects of channel size on the flow field and the slip length are discussed. An erratum to this article can be found at     

Scalable attoliter monodisperse droplet formation using multiphase nano-microfluidics

We demonstrate a robust method to produce monodisperse femtoliter to attoliter droplets by using a nano-microfluidic device. Two immiscible liquids are forced through a nanochannel where a steady nanoscopic liquid filament forms, thinning close to the nanochannel exit to a microchannel due to the capillary focusing. When the nanoscopic filament enters the microchannel, monodisperse droplets are formed by capillary instability. In a certain range of physical parameters and geometrical configurations, the droplet size is only determined by the nanochannel height and independent of liquid flow rates and ratios, surfactants, and continuous phase viscosity. By using nanochannels with a height of 100–900 nm, 0.4–3.5 μm diameter droplets (volume down to 30 aL) have been produced. The generated droplets are stable for at least weeks.     

PIV measurements of flow within plugs in a microchannel

The use of two-phase flow in lab-on-chip devices, where chemical and biological reagents are enclosed within plugs separated from each other by an immiscible fluid, offers significant advantages for the development of devices with high throughput of individual heterogeneous samples. Lab-on-chip devices designed to perform the polymerase chain reaction (PCR) are a prime example of such developments. The internal circulation within the plugs used to transport the reagents affects the efficiency of the chemical reaction within the plug, due to the degree of mixing induced on the reagents by the flow regime. It has been hypothesised in the literature that all plug flows produce internal circulation. This work demonstrates experimentally that this is false. The particle image velocimetry (PIV) technique offers a powerful non-intrusive tool to study such flow fields. This paper presents micro-PIV experiments carried out to study the internal circulation of aqueous plugs in two phase flow within 762 μm internal diameter FEP Teflon tubing with FC-40 as the segmenting fluid. Experiments have been performed and the results are presented for plugs ranging in length from 1 to 13 mm with a bulk mean flow velocity ranging from 0.3 to 50 mm/s. The results demonstrate for the first time that circulation within the plugs is not always present and requires fluidic design considerations to ensure their generation.     

Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids

We report the results of a comparative study of microfluidic emulsification of liquids with different viscosities. Depending on the properties of the fluids and their rates of flow, emulsification occurred in the dripping and jetting regimes. We studied the characteristic features and typical dependence of the size and of the size distribution of droplets in each regime. For each liquid, we identified a range of hydrodynamic conditions promoting generation of highly monodisperse droplets. Viscosity played an important role in emulsification: highly viscous liquids were emulsified into larger droplets with lower polydispersity. Although it was not possible to provide a unified scaling for the volumes of the droplets, our results suggest that the break-up dynamics of the lower viscosity fluids resembles the rate-of-flow-controlled break-up, as reported earlier for the formation of bubbles in flow-focusing geometries [Garstecki P, Stone HA, Whitesides GM (2005) Phys Rev Lett 94:164501]. The results of this study can be helpful for a rationalized selection of liquids for the controlled formation of droplets with a predetermined size and with a narrow distribution of sizes.     

Quantitative comparison of thermal and solutal transport in a T-mixer by FLIM and CFD

The development and adoption of lab-on-a-chip and micro-TAS (total analysis system) techniques requires not only the solving of design and manufacturing issues, but also the introduction of reliable and quantitative methods of analysis. In this work, two complementary tools are applied to the study of thermal and solutal transport in liquids. The experimental determination of the concentration of water in a water–methanol mixture and of the temperature of water in a microfluidic T-mixer are achieved by means of fluorescence lifetime imaging microscopy (FLIM). The results are compared to those of finite volume simulations based on tabulated properties and well-established correlations for the fluid properties. The good correlation between experimental and modelled results demonstrate without ambiguity that (1) the T-mixer is an adiabatic system within the conditions, fluids and flow rates used in this study, (2) buoyancy effects influence the mixing of liquids of different densities at moderate flow rates (Reynolds number Re ≪ 10⁻²), and (3) the combination of FLIM and computational fluid dynamics has the potential to be used to measure the thermal and solutal diffusion coefficients of fluids for a range of temperatures and concentrations in one single experiment. As such, it represents a first step towards the full-field monitoring of both the extent and the kinetics of a chemical reaction.

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Control of serial microfluidic droplet size gradient by step-wise ramping of flow rates

This paper describes a method to control and detect droplet size gradient by step-wise flow rate ramping of water-in-oil droplets in a microfluidic device. The droplets are generated in a cross channel device with two oil inlets and a water inlet. The droplet images are captured and analyzed in a time sequence in order to quantify the droplet generation frequency. It is demonstrated that by controlling the ramping of the oil flow rates it is possible to manipulate the ramping of droplet sizes. Increasing or decreasing of droplet sizes is achieved for a step-wise triangular ramping profile of the oil flow rate. The dynamic behavior of droplets due to the step-wise flow pulses is investigated. Uniform linear size ramping of water-in-oil droplets from 73 to 83 μm in diameter is generated with an oil flow ramping range from 1 to 11 μL/min in a minimum of five steps while water flow rate is held constant at 2 μL/min.     

Formation of fully closed microcapsules as microsensors by microfluidic double emulsion

Microcapsules templated from microfluidic double emulsions attract a great attention due to their broad new potential applications. We present a method to form transparent polymer microcapsules in small sizes of ~30 μm with aqueous cores and fully closed shells. We controlled the size ratio of the aqueous core to the polymer shell not only by flow rates of the double emulsions, but also by synergetic interaction between surfactants at the interface of immiscible fluids. We also found that fully closed shells can be formed by generating the double emulsion droplets in a jetting regime, in which the aqueous cores are confined centrally in the double emulsion droplets. We demonstrated the formation of barcodes in these microcapsules for multiplexed bioassays. These transparent microcapsules also have wide and high potentials for the development of various microsensors by functionalizing the liquid-state cores with compounds sensitive and responsive to temperature, light or electromagnetic field.     

Effect of viscosities of dispersed and continuous phases in microchannel oil-in-water emulsification

Although many aspects of microchannel emulsification have been covered in literature, one major uncharted area is the effect of viscosity of both phases on droplet size in the stable droplet generation regime. It is expected that for droplet formation to take place, the inflow of the continuous phase should be sufficiently fast compared to the outflow of the liquid that is forming the droplet. The ratio of the viscosities was therefore varied by using a range of continuous and dispersed phases, both experimentally and computationally. At high viscosity ratio (η _d/η _c), the droplet size is constant; the inflow of the continuous phase is fast compared to the outflow of the dispersed phase. At lower ratios, the droplet diameter increases, until a viscosity ratio is reached at which droplet formation is no longer possible (the minimal ratio). This was confirmed and elucidated through CFD simulations. The limiting value is shown to be a function of the microchannel design, and this should be adapted to the viscosity of the two fluids that need to be emulsified.     

The Power of Nondeterminism and Randomness for Oblivious Branching Programs

Abstract. This paper abstracts and generalizes the known approaches for proving lower bounds on the size of various variants of oblivious branching programs (oblivious BPs for short), providing an easy-to-use technique which works for all nondeterministic and randomized modes of acceptance. The technique is applied to obtain the following results concerning the power of nondeterminism and randomness for oblivious BPs: <p>— Oblivious read-once BPs, better known as OBDDs (ordered binary decision diagrams), are used in many applications and their structure is well understood in the deterministic case. It has been open so far to compare the power of nondeterministic OBDDs with so-called partitioned BDDs which are a variant of nondeterministic branching programs also used in practice. A k -partitioned BDD has a nondeterministic node at the top by which one out of k deterministic OBDDs with possibly different variable orders is chosen. It is proven here that the two models are incomparable as long as k is bounded by a logarithmic function in the input length. <p>— It is shown that deterministic oblivious read-k -times BPs for an explicitly defined function require superpolynomial size, for k logarithmic in the input length, while there are Las Vegas oblivious read-twice BPs of linear size for this function. This is in contrast to the situation for OBDDs, for which the respective size measures are polynomially related. <p>— Furthermore, an explicitly defined function is presented for which randomized oblivious read-k -times BPs with bounded error require exponential size, while the function as well as its complement can be represented in polynomial size by nondeterministic oblivious read-k -times BPs and deterministic oblivious read-(k+1) -times BPs, where k=o(log n) .